Character contractibility of Banach algebras and homological properties of Banach modules

Rasoul Nasr-Isfahani, and Sima Soltani Renani. "Character contractibility of Banach algebras and homological properties of Banach modules." Studia Mathematica 202.3 (2011): 205-225. <http://eudml.org/doc/286556>.

@article{RasoulNasr2011,
abstract = {Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We give some necessary and sufficient conditions for the left ϕ-contractibility of 𝓐 as well as several hereditary properties. We also study relations between homological properties of some Banach left 𝓐-modules, the left ϕ-contractibility and the right ϕ-amenability of 𝓐. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.},
author = {Rasoul Nasr-Isfahani, Sima Soltani Renani},
journal = {Studia Mathematica},
keywords = {Banach algebra; character amenable; character contractible; injectivity; projectivity; Banach left module; locally compact group},
language = {eng},
number = {3},
pages = {205-225},
title = {Character contractibility of Banach algebras and homological properties of Banach modules},
url = {http://eudml.org/doc/286556},
volume = {202},
year = {2011},
}

TY - JOUR
AU - Rasoul Nasr-Isfahani
AU - Sima Soltani Renani
TI - Character contractibility of Banach algebras and homological properties of Banach modules
JO - Studia Mathematica
PY - 2011
VL - 202
IS - 3
SP - 205
EP - 225
AB - Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We give some necessary and sufficient conditions for the left ϕ-contractibility of 𝓐 as well as several hereditary properties. We also study relations between homological properties of some Banach left 𝓐-modules, the left ϕ-contractibility and the right ϕ-amenability of 𝓐. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.
LA - eng
KW - Banach algebra; character amenable; character contractible; injectivity; projectivity; Banach left module; locally compact group
UR - http://eudml.org/doc/286556
ER -